Transcript PERT/CPM - Pakistan Engineering Council

PERT/CPM
Key Terms

Critical Path: The longest time path through the
task network. The series of tasks (or even a single
task) that dictates the calculated finish date of the
project (That is, when the last task in the critical path
is completed, the project is completed) The
"longest" path (in terms of time) to the completion
of a project. If shortened, it would shorten the time
it takes to complete the project. Activities off the
critical path would not affect completion time even
if they were done more quickly.
2
Slack Time
The amount of time a task can be delayed before the
project finish date is delayed. Total slack can be positive
or negative. If total slack is a positive it indicates the
amount of time that the task can be delayed without
delaying the project finish date. If negative, it indicates
the amount of time that must be saved so that the project
finish date is not delayed. Total Slack = Latest Start Earliest Start. By default and by definition, a task with
0 slack is considered a critical task. If a critical task is
delayed, the project finish date is also delayed. (Also
known as float time)
3
Crashing
Shifting resources to reduce slack time so
the critical path is as short as possible.
Always raises project costs and is
typically disruptive – a project should be
crashed with caution.
4


Gantt Chart: A bar chart. While visually
appealing on a task/duration basis, it is limited
because it does not show task or resource
relationships well. Strength: easy to maintain and
read.
Network Diagram: A wire diagram, Also
known as a PERT network diagram. A diagram
that shows tasks and their relationships. Limited
because it shows only task relationships.
Strength: easy to read task relationships.
5
Sample Gantt Chart
6
Dependencies
Links between project tasks. There are 3 types of
dependencies:

Causal, where 1 task must be completed before
another can begin (have to bake bread before you
can make a sandwich)

critical path schedules are based only on causal
dependencies
Resource, where a task is limited by availability of
resources (more bread can be baked by 2 bakers, but
only 1 is available)
 Discretionary, optional task sequence preferences
that, though not required, may reflect organizational
preferences

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Dummy activity
An imaginary activity with no duration, used to
show either an indirect relationship between 2
tasks or to clarify the identities of the tasks . In
CPM, each activity must be uniquely defined by
its beginning and ending point. When two
activities begin and end at the same time, a
dummy activity (an activity which begins and
ends at the same time) is inserted into the model
to distinguish the two activities.
8
Milestone
A significant task which represents a
key accomplishment within the
project. Typically requires special
attention and control.
9
Work Breakdown Structure (WBS)
A detailed, hierarchical (from general to
specific) tree structure of deliverables and
tasks that need to be performed to
complete a project.
 Purpose: to identify actual tasks to be done
in a project. Serves as basis for project
planning.
 An extension to PERT.

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Work Breakdown Structure



Identify the major task categories
Identify sub-tasks, and sub-sub-tasks
Use verb-noun to imply action to something

Example: Getting up in the morning
Hit snooze button
 Hit snooze button again
 Get outa bed
 Avoid dog
 Go to bathroom…

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Create WBS



Decomposition of project deliverables and
activities into smaller, more manageable parts
The lowest level in WBS is a Work Package
based on Statement Of Work (SOW)
Needs to be S.M.A.R.T (Specific,
Measurable, Attainable, Realistic, Timely)
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Work Breakdown Structure
Canoe Trip to
Boundary Waters
Arrange Travel
Get Equipment
Schedule Flights to Mpls
Plan Meals
Plan Activities
Bring cooking gear
Assign Budget Person
Obtain
emerg. #’s
Bring Cards
Freeze dry food
Get deposits
Arrange
contact at BW
Bring
Joke book
Prepare 7
breakfasts
Retain Receipts
Bring
emerg. flares
Bring scotch
Bring
Sleeping Bags
Prepare 7 lunches
Pay for supplies
Bring two
first aid kits
Bring
Fishing Gear
Prepare 6 dinners
Close-out trip
Contact BW Outfitter
Rent Van
Rent canoes
Arrange Motel
Rent Tents
Schedule return flights
Plan for
Emergencies
Prepare Budget
Bring lights and
waterproof
matches
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Work Breakdown Structure
Canoe Trip to
Boundary Waters
Arrange Travel
Get Equipment
Schedule Flights to Mpls
Plan Meals
Plan Activities
Bring cooking gear
Assign Budget Person
Obtain
emerg. #’s
Bring Cards
Freeze dry food
Get deposits
Arrange
contact at BW
Bring
Joke book
Prepare 7
breakfasts
Retain Receipts
Bring
emerg. flares
Bring scotch
Bring
Sleeping Bags
Prepare 7 lunches
Pay for supplies
Bring two
first aid kits
Bring
Fishing Gear
Prepare 6 dinners
Close-out trip
Contact BW Outfitter
Rent Van
Rent canoes
Arrange Motel
Rent Tents
Schedule return flights
Plan for
Emergencies
Prepare Budget
Bring lights and
waterproof
matches
15
Work Breakdown Structure
Canoe Trip to
Boundary Waters
Arrange Travel
Get Equipment
Schedule Flights to Mpls
Plan Meals
Plan Activities
Bring cooking gear
Assign Budget Person
Obtain
emerg. #’s
Bring Cards
Freeze dry food
Get deposits
Arrange
contact at BW
Bring
Joke book
Prepare 7
breakfasts
Retain Receipts
Bring
emerg. flares
Bring scotch
Bring
Sleeping Bags
Prepare 7 lunches
Pay for supplies
Bring two
first aid kits
Bring
Fishing Gear
Prepare 6 dinners
Close-out trip
Contact BW Outfitter
Rent Van
Rent canoes
Arrange Motel
Rent Tents
Schedule return flights
Plan for
Emergencies
Prepare Budget
Bring lights and
waterproof
matches
16
Work Breakdown Structure
Canoe Trip to
Boundary Waters
Arrange Travel
Get Equipment
Schedule Flights to Mpls
Plan Meals
Plan Activities
Bring cooking gear
Assign Budget Person
Obtain
emerg. #’s
Bring Cards
Freeze dry food
Get deposits
Arrange
contact at BW
Bring
Joke book
Prepare 7
breakfasts
Retain Receipts
Bring
emerg. flares
Bring scotch
Bring
Sleeping Bags
Prepare 7 lunches
Pay for supplies
Bring two
first aid kits
Bring
Fishing Gear
Prepare 6 dinners
Close-out trip
Contact BW Outfitter
Rent Van
Rent canoes
Arrange Motel
Rent Tents
Schedule return flights
Plan for
Emergencies
Prepare Budget
Bring lights and
waterproof
matches
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Work Breakdown Structure
System Hardware Replacement
RFP Development
Vendor Selection
Staff Training
Hardware Implementation
Needs Assessment
Research Vendors
Identify training Plan
Schedule Installation
Needs Analysis
Research Sites
Schedule Training
Prepare Site
Write RFP
Select Vendors to mail RFP
Train
Arrange Vendor Support
Finalize with Purchasing
Review Proposals
Configure System
Rank Proposals
Install System
Recommendation
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Work Breakdown Structure
System Hardware Replacement
RFP Development
Vendor Selection
Staff Training
Hardware Implementation
Assess Needs
Research Vendors
Identify training Plan
Schedule Installation
Analyze Needs
Research Sites
Schedule Training
Prepare Site
Write RFP
Select Vendors to mail RFP
Train Sysadmins
Arrange Vendor Support
Finalize with Purchasing
Review Proposals
Configure System
Rank Proposals
Install System
Make Recommendations
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Work Breakdown Structure

Requires structured brainstorming
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WBS Dictionary


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

A companion document to the WBS
May have detailed content of the components
contained in a WBS, including work packages and
control accounts
For each WBS component, the WBS dictionary
includes a code of account identifier, a statement of
work, responsible organization, and a list of
schedule milestones
Can include a list of associated schedule activities,
resources required, and an estimate of cost
Each WBS component is cross-referenced, as
appropriate, to other WBS components
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Project Management Assumptions

PM makes several key assumptions







All tasks have distinct begin and end points
All estimates can be mathematically derived
Tasks must be able to be arranged in a defined sequence that
produces a pre-defined result
Resources may be shifted to meet need
Cost and time share a direct relationship (Cost of each
activity is evenly spread over time)
Time, of itself, has no value
These assumptions make PM controversial
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THE PM Concept Assumption
A Critical Path Exists



A small set of activities, which make up the
longest path through the activity network
control the entire project.
If these "critical" activities could be identified
& assigned to responsible persons, management
resources could be optimally used by
concentrating on the few activities which
determine the fate of the entire project.
Others can be re-planned, rescheduled &
resources for them can be reallocated, without
affecting the project.
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Standardized PM Tools

1917: Henry Gantt introduced standardized PM
tools
Gantt Chart – visual tracking of tasks and resources
 Depiction of relationships between tasks
 Depiction of constraints between tasks
 First Widespread acceptance of a single technique


Created out of need and frustration as
industrialization became ever more complex
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PERT & CPM

PERT (Program Evaluation and Review Technique) –
introduced by US military (Navy) in 1958

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CPM (Critical Path Method) – introduced by US industry
in 1958 (DuPont Corporation and Remington-Rand)


Industry: control costs and schedules in manufacturing
Common weakness to both: ignores most dependencies


US Navy : control costs & schedules for Polaris Submarine construction
Considers only completion of a preceding required task
Both rely on a logical sequence of tasks

Organized visually (Charts), tabular or simple lists
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An Example of a Logical Sequence
Making a simple list of tasks
Planting
trees with
flowers and edging
around them – tasks
required to complete
this project:
1. Mark utilities, 2. Dig
Holes, 3. Buy trees, 4. Buy
flowers, 5. Plant trees, 6.
Plant flowers, 7. Buy
edging, 8. Install edging



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
This list does not reflect
time or money
This list does not reflect
task relationships
This list is a simple
sequence of logical
events
This list does not
provide an easy project
“snapshot”
Hard to see conflicts
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An Example of a Logical Sequence
Tabular – including time and cost data
Normal Time
(Days)
Crashed Time
(Days)
Normal Cost
($)
Crashed Cost
($)
Mark Utilities
3
3
0
0
Dig Holes
2
1
100
200
Buy Trees
.5
.5
50
50
Buy Flowers
.5
.5
50
50
Plant Trees
2
1
100
200
Plant Flowers
1
.5
50
100
Buy Edging
.5
.5
25
25
Install Edging
1
.5
25
50
10
6
400
675
Task Name
TOTALS
NOTE: Shaded areas are concurrent tasks that are completed along the
timeline- they contribute to overall cost but not overall duration
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An Example of a Logical Sequence
Visual - Using a PERT Chart (Network Diagram)
Planting trees with flowers and edging around them
Visual – task relationships are clear – good snapshot
7
Buy
Edging
3
1
Mark
Utilities
2
Dig Holes
5
6
8
Plant
Trees
Plant
Flowers
Install
Edging
END
START
Buy Trees
4
Buy
Flowers
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Variation in Networks
 Standards
such as BS 6046
 Activity on Arrow
 Activity on Node
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7
1
2
5
6
8
END
START
3
4
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Early Start
Duration
Early Finish
Early
Start
Task Name
Duration
Early
Finish
3 Buy Trees
Late Start
Slack
Late Finish
0
Late Start
3
Slack
3
Early
Start
1 Mark Utilities
2
Early
Finish
Duration
2 Dig Holes
Late Start
2
Late
Finish
Late
Finish
Slack
5
Early
Start
Duration
Early
Finish
4 Buy Flowers
Late Start
Slack
Late
Finish
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3
0
3
3
.5
0
3
3
.5
3.5
3 Buy Trees
7 Buy Edging
LS Slack LF
LS Slack LF
3
2
5
5
2
7
2 Dig Holes
5 Plant Trees
3
5
1 Mark Utilities
0
3.5
3
0
5
.5
3.5
0
7
7
1
8
6 Plant Flowers
7
0
8
8
1
9
8 Install Edging
8
0
4 Buy Flowers
LS Slack LF
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9
Forward and Backward Pass




Forward pass is a technique to move forward through a
diagram to calculate activity duration. Backward pass is
its opposite.
Early Start (ES) and Early Finish (EF) use the
forward pass technique.
Late Start (LS) and Late Finish(LF) use the
backward pass technique.
MEMORY TRIGGER: if the float of the activity is
zero, the two starts (ES and LS) and the two finish (EF and
LF) are the same. Hence, If float of activity is zero, ES =
LS and EF = LF.
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PM Today – Necessary?



Frustration with cost & schedule overruns
Frustration with reliability of production estimates
Management challenges exist today:

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
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Only 44% of projects are completed on time
On average, projects are 189% over-budget
70% of completed projects do not perform as expected
30% of projects are canceled before completion
On average, projects are 222% longer than expected
PM has been shown to improve this performance
These statistics were compiled by an independent monitoring group, The Standish Group, and
represent the US national average for 1998
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PERT/CPM
CALCULATIONS
Basic Techniques
PERT Calculations


Step 1: Define tasks
Step 2: Place Tasks in a logical order, find the critical path


Step 3: Generate estimates





The longest time path through the task network. The series of tasks (or
even a single task) that dictates the calculated finish date
Optimistic, pessimistic, likely and PERT- expected
Standard Deviation and variance
Step 4: Determine earliest and latest dates
Step 5:Determine probability of meeting expected date
Steps 1 and 2 are logic and legwork, not calculation – these
require a clear goal
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PERT Calculations – Step 3



Assuming steps 1 and 2 have been completed begin calculations –
use a table to organize your calculations
Simple calculations to estimate project durations
Based on input of 3 estimated durations per task

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
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Formula derives a probability-based expected duration (TE)


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Most Optimistic (TO) – best case scenario
Most Likely (TL) “normal” scenario
Most Pessimistic (TP) Worst case scenario
(TO x 1 + TL x 4 + TP x 1) / 6 = TE
Read this formula as the sum of (optimistic x 1 + likely x 4 + pessimistic x 1)
divided by 6 = expected task duration
Complete this calculation for all tasks
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PERT Calculations – Step 3

Standard deviation and variance

Standard deviation (SD) is the average deviation
from the estimated time
SD=(TP-T0)/6 {read as (pessimistic-optimistic)/6}
 As a general rule, the higher the standard deviation the
greater the amount of uncertainty


Variance (V) reflects the spread of a value over a
normal distribution

V=SD2 (Standard deviation squared)
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PERT Calculations – Step 3


When doing manual PERT Calculations it is helpful to
construct a table to stay organized
Consider the sample project– planting trees and
flowers, set up using a list
 Rough estimates and no risk analysis

No Range, simply rough estimates - unreliable?
PERT Analysis will better refine estimates
Start by setting up a table to organize data


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Our Project – A Refresher
TASK ID
Set up in tabular form, it
might look like this…
Description
1
Mark Utilities
2
Dig Holes
3
Buy Trees
4
Buy Flowers
5
Plant Trees
6
Plant Flowers
7
Buy Edging
8
Install Edging
Duration (Days)
?
?
?
?
?
?
?
?
7
Buy
Edging
3
1
Mark
Utilities
2
Dig Holes
4
Buy
Flowers
5
6
8
Plant
Trees
Plant
Flowers
Install
Edging
END
START
Buy Trees
Set up in visual form it might
look like this…
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PERT Step 3– First Get Organized
In considering all tasks on the previous slide, a table might look like this
TASK
1
2
5
6
8
TOTAL
TASK
3
4
7
TOTAL
TO
TO
TO-Optimistic
CRITICAL PATH TASKS (Longest Duration)
TL
TP
TE
TL
TP
TM-Likely
OTHER PROJECT TASKS
TE
TP-Pessimistic TE-Expected (Derived by PERT)
Remember – tasks 3, 4 and 7 are concurrent and do not add to the timeline
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PERT Step 3– Durations
After generating estimates using the formula, the table might look like this
TASK
1
2
5
6
8
TOTAL
TO
1
2
1
1
1
7
TASK
3
4
7
TOTAL
TO
.5
.5
.5
1.5
TO-Optimistic
CRITICAL PATH TASKS (Longest Duration)
TL
TP
TE
3
5
3
4
7
4.17
3
6
3.17
3
5
3
2
4
2.17
15
28 15.6
OTHER PROJECT TASKS
TL
TP
TE
1
3
1.25
1
3
1.25
1
3
1.25
3
9
3.75
TM-Likely
SD=Standard Deviation
SD
.67
.83
.83
.67
.5
3.5
V
.44
.69
.69
.44
.25
2.51
SD
.42
.42
.42
1.26
V
.17
.17
.17
.51
TP-Pessimistic TE-Expected (Derived by PERT)
V=Variance
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PERT Step 4 – Dates
For each task, determine the latest allowable time for moving to the next task
The difference between latest time and expected time is called slack time
Tasks with zero slack time are on the critical path
TASK
1
2
5
6
8
TOTAL
TO
1
2
1
1
1
7
TASK
3
4
7
TOTAL
TO
.5
.5
.5
1.5
CRITICAL PATH TASKS (Longest Duration)
TL
TP
TE
ES
EF
LS
LF
Slack
3
5
3
0
3
0
3
0
4
7
4.17
3
7.17
3
7.17
0
3
6
3.17
7
10.17
7
10.17
0
3
5
3
10
13
10
13
0
2
4
2.17
13
15.17
13
15.17
0
15
28 15.51
OTHER PROJECT TASKS
TL
TP
TE
ES
EF
LS
LF
FLOAT
1
3
1.25
0
1.25
3
4.25
3
1
3
1.25
0
1.25
3
4.25
3
1
3
1.25
1.25
2.50 4.25 5.50
3
3
9
3.75
ES=Earliest Start EF=
Earliest Finish
LS=Latest Start
SD
.67
.83
.83
.67
.5
3.5
V
.444
.694
.694
.444
.254
2.530
SD
.42
.42
.42
1.26
V
.17
.17
.17
.51
LF=Latest Finish
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PERT Step 5 – Probabilities
Manually computing probability using data compiled in your table

Determine probability of meeting a date by using the table data





Denote the sum of all expected durations on the critical path as S
Denote the sum of all variances on the critical path as V
Select a desired completion time, denote this as D
COMPUTE: (D-S)/square root (V) = Z ( the number of std. deviations that the due date is
away from the expected date))
Enter a standard normal table to find a probability that corresponds with Z
PZ  z 
z





1
 1 2
exp(  Z  dZ
2
 2 
For our project, figure a probability based on the most likely time, 15 days: (1515.51)/square root(2.53) = (15-15.51)/1.59=-.3207 (Z)
A corresponding probability is 37.7% (Rounded)
This process can be repeated for any date desired
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PERT Step 5 – Probabilities
Computing probability in Excel using data compiled in your table



Microsoft Excel has normal distribution
functions built in and can compute PERT
probabilities
By creating a table as a spreadsheet, the addition
of a few simple formulae will do the rest of the
work
Create a table as a template that can be used over
and over again – simply change the input
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